euclidean distance between two points with different dimensions

If I have 2 points one is 2d point (1,2) and another 3d point (1,2,4) is there a way to measure the distance or the euclidean distance between them?

Any suggestions on how to measure the distances between two different point with different dimensions?

[John BG]

have you considered that both points have same dimensions?

the points you call 2D have 3rd dimension zeroed

[CC_had]

no, both points have different dimensions.

Answer 1

[Star Strider]

You would have to ‘create’ a third dimension for the first point (perhaps (1,2,0) to calculate its distance from the second (1,2,4). You cannot calculate the Euclidean distance between points with different dimensions.

[Image Analyst]

Unless the "point" was actually a line along the 3rd dimension and you used the point-to-line distance formula https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line but I don't think CC_had meant this situation.

[CC_had]

I am using pca eiginfaces and I am trying to plot the real face and all the reconstructed photo in the same plot. and I want to measure the euclidean distance between the real and the reconstructed ones. each of the reconstructed ones have different dimensions that why I don't know how to do that?

[Star Strider]

To the best of my knowledge, you cannot calculate Euclidean distances between objects with different dimensions. I do not know of any metric that would allow you to do that.